I've seen similar problems from a corroded battery cable, connector, or battery terminal.

Pull both cables off, give them a very good cleaning, rough up the battery terminals, and re-tighten.

I had one battery cable, looked ok, but a twist of the connector at the end of the cable and the wire just disintegrated, it was completely corroded inside. Turns out the battery terminal had been cracked, and was leaking a tiny bit of battery acid right at the terminal for a while.